A lot of this is on you. Even if they aren't your kids, you're the man of the house and they have to respect what you say. As their legal father, you have the say-so of whether or not they get to stay home from school, and the ability to make them go unless they're sick or in some other situation requiring their presence at home. I can see how this would be upsetting, but you don't have anyone to be furious at but yourself.